Standard
Class Standard_LambdaJulia

Object
  common:Generic
      common:Formula
          common:DivergentFormula
              Standard:Standard_LambdaJulia

class 
DivergentFormula:Standard_LambdaJulia

Object version of LambdaJulia in Standard.ufm. Alternative Julia set that iterates the classical Logistics equation using complex numbers. All Julia sets created with this type can be recreated with the classical Julia set, but the parameters work differently, and the corresponding Mandelbrot set is different, too. Originally written by Damien M. Jones.

Ultra Fractal Source

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 class Standard_LambdaJulia(common.ulb:DivergentFormula) {
 ;
 ; Object version of LambdaJulia in Standard.ufm.
 ;
 ; Alternative Julia set that iterates the classical Logistics
 ; equation using complex numbers. All Julia sets created with
 ; this type can be recreated with the classical Julia set,
 ; but the parameters work differently, and the corresponding
 ; Mandelbrot set is different, too.
 ;
 ; Originally written by Damien M. Jones.
 ;
 public:
   complex func Init(complex pz)
     return pz
   endfunc
 
   complex func Iterate(complex pz)
     return @seed * pz * (1 - pz) ^ (@p_power - 1)
   endfunc
 
 default:
   title = "Lambda (Julia)"
   helpfile = "Uf*.chm"
   helptopic = "Html/formulas/standard/lambda.html"
   param seed
     caption = "Julia Seed"
     default = (1,0)
     hint = "Use this parameter to create many different Julia sets. A good \
             way to set this parameter is with the Eyedropper or Explore features."
   endparam
   param p_power ; Overrides p_power from Formula
     caption = "Exponent"
     default = (2,0)
     hint = "This parameter sets the exponent for the Julia formula. \
             Increasing the real part to 3, 4, and so on, will multiply the \
             symmetry of the Julia figure. Non-integer real values and non-zero \
             imaginary values will create distorted Julia fractals. Use (2, 0) \
             for the standard Julia set."
   endparam
   param p_bailout ; Overrides p_bailout from DivergentFormula
     caption = "Bailout"
     default = 1.0e20
     exponential = true
     hint = "This parameter defines how soon an orbit bails out while \
             iterating. Larger values give smoother outlines; values around 4 \
             give more interesting shapes around the set. Values less than 4 \
             will distort the fractal."
   endparam
 }
 

Constructor Summary

Standard_LambdaJulia()

Method Summary

complex	Init(complex pz) Set up for a sequence of values
complex	Iterate(complex pz) Produce the next value in the sequence

Methods inherited from class common:DivergentFormula

GetUpperBailout, IsBailedOut

Methods inherited from class common:Formula

GetLowerBailout, GetPrimaryExponent

Methods inherited from class common:Generic

GetParent

Methods inherited from class Object

Constructor Detail

Standard_LambdaJulia

public Standard_LambdaJulia()

Method Detail

Init

public complex Init(complex pz)

Description copied from class: DivergentFormula

Set up for a sequence of values

This function will be called at the beginning of each sequence of values (e.g. at the beginning of each fractal orbit).

Overrides:

Init in class DivergentFormula

Parameters:

pz - seed value for the sequence; for a normal fractal formula, this will be #pixel

Returns:

first value in the sequence; this corresponds to #z in a fractal formula

Iterate

public complex Iterate(complex pz)

Description copied from class: Formula

Produce the next value in the sequence

As long as the sequence has not bailed out, this function will be continually called to produce sequence values.

Overrides:

Iterate in class Formula

Parameters:

pz - previous value in the sequence; corresponds to #z in a fractal formula. Note that you should always use this value for computing the next iteration, rather than a saved value, as the calling code may modify the returned value before passing it back to the next Iterate() call.

Returns:

the next value in the sequence